Reduce to lowest terms: $- \dfrac{1}{9} \div \dfrac{9}{5} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{9}{5}$ is $ \dfrac{5}{9}$ Therefore: $ - \dfrac{1}{9} \div \dfrac{9}{5} = - \dfrac{1}{9} \times \dfrac{5}{9} $ $ \phantom{- \dfrac{1}{9} \times \dfrac{5}{9}} = \dfrac{-1 \times 5}{9 \times 9} $ $ \phantom{- \dfrac{1}{9} \times \dfrac{5}{9}} = \dfrac{-5}{81} $